I saw the following sentence in a dialogue:
Wir sind zum Besuch hier
Is this a common construction to describe one's purpose of being somewhere, or doing something? Is there a formal name for this construction? Can you do this with any noun, and is it used in this format?
Ich bin zum (Noun) hier?
It should be zu Besuch, which is more of a fixed expression.
Otherwise, yes it can be used with many nouns to express a purpose. Zum (zu dem) and zur (zu der) are contractions that are used in conjunction with words of their respective genus (zum: masculine, neutral; zur: feminine).
Nominalized verbs (Putzen, Arbeiten) always have a neutral genus and are, hence, used with zum (zum Putzen, zum Arbeiten). In contrast, Arbeit (die Arbeit) is used with zur (zur Arbeit) because it is feminine. Words nominalized with -ung are feminine, and thus also require zur.
Ich bin zum Arbeiten hier.
(zum Putzen, zum Abholen, zum Aufräumen, zum Grillen)Ich bin zur Arbeit hier.
(zur Erholung, zur Weiterbildung, zur Gerichtsverhandlung, zur Wohnungsendabnahme, zur Hochzeit, zur Geburtstagsfeier)
